In the CBR literature from the past 25 years there is a considerable amount of research work that makes use of cases that are subspaces of some representation space rather than points in it. For cases of that kind, different terms n used such as generalized case, prototype, schema, script, or abstract case. Our analysis of selected publications yields that on the one hand the same term is used for different concepts and on the other hand different terms are used for more or less the same concepts. So our goal is to improve the conceptual clarity by proposing an integrated classification schema for cases. We then use this schema to describe semantically founded ways for similarity definition and computation, depending on the class membership of query and case.